Marie Jean Antoine Nicolas de Caritat Condorcet

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17 September 1743
Ribemont, France
29 March 1794
Bourg-la-Reine (near Paris), France

The Marquis de Condorcet's most important work was on probability and the philosophy of mathematics.


Marie-Jean-Antoine-Nicolas de Caritat took his hereditary title Marquis de Condorcet from the town of Condorcet in Dauphiné. His parents were Jean Pierre Antoine Caritat de Condorcet (1702-1743) and Marie Madeleine Catherine Gaudry (1710-1784). Antoine Caritat de Condorcet was a military man and was captain of the Barbançon regiment. He married Madeleine Gaudry on 12 March 1740 in Ribemont. Madeleine had been born in Ribemont on 30 January 1710 and had married her first husband Fulcrand Philippe Etienne de Saint Félixon on 3 January 1731. He had been killed at the Battle of Gastalla, in Italy, on 19 September 1734. Antoine was then Madeleine's second husband but, sadly, he was killed on manoeuvres near Neuf Brisach, France, on 22 October 1743, only five weeks after the birth of their only child Marie Jean Antoine Nicolas de Caritat, the subject of this biography. The noble Condorcet family had undergone forced religious changes which are worth mentioning since they almost certainly had an impact on the young child. Henri de Caritat, his great-great-great-great grandfather, had adopted the Reformed faith as early as 1561 but when France turned against the Huguenots some members of the Condorcet family fled France while those was remained converted back to Roman Catholicism. Condorcet, as we will refer to the subject of this biography, came from the branch re-converted to Catholicism and, had he followed the family tradition, he would have joined the military or the Church, the only two occupations deemed suitable to the nobility.

Condorcet's mother was a deeply religious woman and she dedicated her son to the Virgin Mary and treated him in an extremely protective manner, understandable after the loss of two husbands. She continued to dress Condorcet as a baby in white dresses until he was eight years old. He was kept away from others and denied the exercise and open air play that young boys would enjoy. Up to the age of eight he received some instruction from his mother but his uncle, Bishop Jacques-Marie de Caritat de Condorcet, worried that the young boy was not getting a proper education, arranged for a Jesuit tutor to teach the boy at his home from the age of nine to eleven. In 1754 Condorcet entered the Jesuit College in Reims where he spent four years. His achievements at this College were very good but not quite as exceptional as one might have expected given his later genius; he gained a second prize at the age of thirteen. His ideas about education, as given in On the Nature and Purpose of Public Instruction (1791), are relevant to his performance at school (see for example [5]:-
Human life is not a struggle in which rivals contend for prizes. It is a voyage that brothers make together: where each employs his forces for the good of all and is rewarded by the sweetness of mutual benevolence, by the pleasure that comes with the sentiment of having earned the gratitude or the esteem of others ... By contrast, the crowns bestowed in our colleges - which induce the schoolboy to believe himself already a great man - only arouse a childish vanity from which a wise system of instruction would seek to preserve us if, by misfortune, its origin lay in our nature and not in our blundering institutions. The habit of striving for first place is either ridiculous or unfortunate for the individual in whom it has been inculcated.
Also relevant to these years of his education is the fact that, in later life, he argued strongly against education being run by the Church.

In 1758 Condorcet entered the Collège de Navarre in Paris which had a high academic reputation. A recent development had been in 1753 when Jean-Antoine Nollet (1700-1770) had been appointed as the first professor of experimental physics and had taught in a specially constructed lecture theatre for 600 students. Breaking with the tradition that all teaching had been in Latin, Nollet insisted that physics be taught in French. Georges Girault de Kéroudou taught mathematics and philosophy at the Collège de Navarre and he gave Condorcet a passion for mathematics so, when he graduated from the Collège de Navarre in 1760, he was determined to pursue a career in mathematics. His family, however, were very strongly opposed to such a career feeling that this was totally against the spirit of the hereditary nature of the noble standing of "de Condorcet." He spent two years back at his home in Ribemont studying mathematics on his own, arguing to be allowed to pursue a career in mathematics and science and, eventually, he prevailed.

In 1762 Condorcet left his home in Ribemont and went to Paris where he lived with Georges Girault de Kéroudou who had taught him mathematics at the Collège de Navarre. Condorcet lived in a small attic above Girault de Kéroudou's home on the rue de Jacob in central Paris, close to the University. Jeanne Julie Éléonore de Lespinasse (1732-1776), who ran a salon in Paris and became famed as a letter writer, was a close friend of Jean le Rond d'Alembert and she got to know Condorcet well at this time. She described him as [3]:-
... a great hulking gawky youth, shy and embarrassed in manner, who walked stooping, bit his nails, blushed when spoken to, and either said nothing in reply or else spoke low and fast.
We leave the reader to judge how much of his manner at the time was a result of his very protective upbringing. Condorcet was now undertaking research on the integral calculus and he produced a memoir which was refereed by Alexis Claude Clairaut and Alexis Fontaine. They saw much potential in the young Condorcet, but rejected the paper with, however, encouragement and advice on how he should proceed.

In 1765 Condorcet's memoir Essai sur le calcul intégral was submitted to the Académie des Sciences and refereed by d'Alembert and Étienne Bézout who reported positively on 22 May 1765. They write:-
M de Condorcet ... fully resolves this general problem: "Given a differential equation of a given order, which contains as many variables as one wishes, determine whether this equation, in the state in which it is proposed, admits, or does not admit, an integral of an immediately lower degree." The solution he gives of this problem, in addition to having the merit of utility, has the merit of elegance and of generality. ... The work announces the greatest talents, and those most worthy of being stimulated by the approval of the Academy.
Condorcet gives the following Preface to the work:-
I propose in this work to give a general method of determining the finite integral of a given differential equation. I divide it into two parts. I will deal in the first, with sufficient scope, with ordinary differential equations: in the second I will give some principles for applying the theory explained in the first part to finite difference equations, and to those where the same variable, equal to a function of several others, has been successively assumed to vary with each of them.
In the acknowledgements he thanks Alexis Fontaine for his "kindness to communicate to me, before the printing of his Memoirs, the fundamental Theorem which is found there on page 24." He also notes connections of his work on difference equations to results of d'Alembert in his memoir Recherches sur Differens Points Importans du Systeme du Monde (1754-56) and to Euler in his Institutions Calculi Differentialis (1755). He adds:-
The partial difference equations for which I give some principles, were first treated from a different point of view in the dissertation 'Reflexions sur la Cause Generale des Vents' (1747) of M d'Alembert. There several of these equations are integrated by a very ingenious method, which combines elegance with simplicity. M M Euler and Lagrange have since solved some by other methods. Those of the latter have a very great generality, and its author has applied them to very complicated equations.
As a result of this memoir and a series of other mathematics papers he published at this time, Condorcet was elected to the Académie des Sciences in 1769. Around this time he was a frequent visitor to Julie de Lespinasse's salon which she had opened on the rue de Belle Chasse in 1764. This salon was justly described as the "laboratory of the Encyclopaedia" for here aristocrats, diplomats, philosophers, mathematicians and politicians met. Condorcet would have deep mathematical discussions with d'Alembert who was living in Julie de Lespinasse's salon. He produced several important works, including one in 1772 on the integral calculus which was described by Lagrange as [see Arago's 'Biographie de Condorcet' in the Académie des Sciences]:-
... filled with sublime and fruitful ideas which could have furnished material for several works. The last article particularly pleased me for its elegance and its utility. ... The recurring series had already been treated so often that one would have said that this matter had been exhausted. However, here is a new application of these series, more important, in my opinion, than any that we have already made. It opens up, so to speak, a new field for the perfection of 'Integral Calculus'.
Soon after the publication of his 1772 work, Condorcet met Anne Robert Jacques Turgot (1727-1781), a French economist, in Julie de Lespinasse's salon. Turgot had become an administrator under Louis XV and was appointed Controller General of Finances in August 1774 under Louis XVI. In the year he was appointed, he had Condorcet appointed Inspector General of the Mint. This marks a major change in direction in Condorcet's career. Up to that time he had devoted himself entirely to mathematics, but from then on, although he continued to make mathematical contributions, he was occupied with other roles and a variety of other academic interests [49]:-
At the time of Turgot's ministry of 1774-76, [Condorcet] published a sequence of works on economic subjects, including the grain trade (1774), the corvée tax (1775), monopoly (1775), deregulation (1775), and, again, the grain trade (1776).
Turgot was dismissed from his post in 1776 and Condorcet tended his resignation in support. Condorcet's resignation, however, was refused and he continued to fill this post until 1791.

In 1777 Condorcet was appointed Secretary of the Académie des Sciences. He had been advised by Voltaire and by d'Alembert to become an expert in writing obituaries in order to improve his chances of getting the post. It certainly was good advice and the large number of obituaries he wrote were highly praised, but nevertheless it severely curtailed his mathematical output.

His most important work was on probability and the philosophy of mathematics, especially his treatise Essay on the Application of Analysis to the Probability of Majority Decisions (1785). This is an extremely important work in the development of the theory of probability [49]:-
Condorcet's 'Essai' of 1785 was dedicated to Turgot. and he presented it as an attempt to demonstrate the applicability of calculation to "questions of interest for common utility". It was concerned explicitly, as Condorcet explains at the beginning of the introduction, with the practice, widespread since antiquity, of submitting all individuals to the will of the greatest number. It was also concerned with the differences between ancient and modem constitutions to which Condorcet returned throughout the rest of his life ... The justification for majority voting in the ancient constitutions, Condorcet wrote in the 'Essai', was associated with "the words 'freedom' and 'utility'," more than with '''truth' and 'justice'." ...

Condorcet makes clear, in the introduction to the 'Essai', that the decisions to be made in modem constitutions are about important social questions, including economic policy. He gives four examples of the difficulty in democratic procedures that is now known as his impossibility result, or his demonstration of the impossibility of finding a "Condorcet winner" (under certain distributions of preferences, in which every candidate in a majority election will be defeated by some other candidate.)
The final of Condorcet's examples is today known as the 'Condorcet Paradox'. It points out that it is possible that a majority prefers option A over option B, a majority prefers option B over option C, and yet a majority prefers option C over option A. (Thus, "majority prefers" is not transitive.)

Condorcet published Vie de M Turgot (1786) and Vie de Voltaire (1789). In these biographies he showed that he favoured Turgot's economic theories and agreed with Voltaire in his opposition to the Church. Also in 1786 he again worked on his ideas for the differential and integral calculus, giving a new treatment of infinitesimals. However his treatise was never printed.

On 28 December 1786, Condorcet married Marie Louise Sophie de Grouchy in the Chapelle du Château de Villette, Condécourt, Île-de-France. Sophie de Grouchy (1764-1822) was the daughter of François Jacques de Grouchy (1715-1808) and Marie Gilberte Henriette Freteau de Peny (about 1740-1793). Joan Landes writes [41]:-
Like her husband, de Grouchy was committed to bringing about major judicial and political reforms in France; and her own experiences at a convent left her with a similarly fierce dislike of the Church and a commitment to secular values. The two met through their common interest in the defence of three peasant victims of judicial error and legal abuse ... whose cause had been taken up by de Grouchy's uncle, the magistrate Charles Dupaty, president of the parliament of Bordeaux. ... Mme de Condorcet was an accomplished translator and author, in her own right; and she shared her husband's liberal and republican views, especially on matters of criminal justice, political reform, and minority and women's rights.
On the 24 April 1790 Antoine and Sophie de Caritat de Condorcet's only child, Alexandrine-Louise-Sophie de Caritat de Condorcet (1790-1859), was born at the Hôtel des Monnaies at 11 Quai de Conti, Paris. This was the building housing the Paris Mint. Known as Élisa, she was baptised on the following day with Louis Alexandre, Duke of Rochefoucauld, as her godfather, and Marie Henriette Gilberte Freteau, represented by her daughter, Charlotte Félicité de Grouchy, as godmother. When she was seventeen years old, Élisa married Arthur O'Connor (1763-1852) in Paris on 4 July 1807. He was born in Cork, Ireland, had gone to France to seek support for an Irish revolution and had been appointed to the French army by Napoleon.

The year 1789 saw the outbreak of the French Revolution when in May of that year France became a constitutional monarchy followed by the storming of the Bastille on 14 July. Condorcet championed the liberal cause, he was elected as the Paris representative in the Legislative Assembly and he became the secretary of the Assembly. He drew up plans for a state education system which were given only a little attention due to the political situation of France at the time. In this report he writes (see [33]):-
To offer all individuals of the human race the means to provide for their needs, to ensure their well-being, to know and exercise their rights, to understand and fulfil their duties, to ensure for each one the faculty of perfecting his industry, to render himself capable of the social functions to which he has the right to be called, to develop the whole range of talents with which nature has endowed him, and by this means to establish between all citizens an equality of fact and to realise the political equality recognised by the law - this must be the first goal of national educational system.
He published Sur l'admission des femmes au droit de cité in 1790, the year his daughter was born. Guillaume Ansart writes about this work in [20]:-
From a political perspective, Condorcet insists, there are no fundamental differences between the sexes. Sexual and gender differences are either the product of education and socialisation - and therefore subject to change - or they are simply irrelevant to a discussion of natural rights. The first category includes the different spheres of activity (public versus private) to which men and women have traditionally applied their intellect, as well as their allegedly different senses of morality or justice. Women, it has been said, are guided by their feelings rather than by their reason or conscience. But such differences, Condorcet asserts, are caused by purely social factors: generally excluded from public life, women have directed their intelligence toward different objects and therefore may have developed, for instance, a different sense of justice from that of me ...[Condorcet writes] "if reasons such as these were admitted against women, it would also be necessary to deprive of the rights of citizenship that portion of the people who, because they are occupied in constant labour, can neither acquire knowledge nor exercise their reason. Soon, little by little, only persons who had taken a course in public law would be permitted to be citizens."
By 1792 Condorcet had become one of the leaders of the Republican cause. He joined the moderate Girondists and argued strongly that the King's life should be spared. When the Girondists fell from favour and the Jacobins, a more radical political group led by Robespierre, took over, Condorcet argued strongly against the new, hurriedly written, constitution which was drawn up to replace the one which he himself had been chiefly responsible for drawing up. This showed a lack of common sense and he paid for it when a warrant was issued for his arrest.

In the period to the run-up to his arrest he wrote Tableau général . The authors of [32] write:-
Condorcet wrote 'Tableau général' in haste during a few days in spring-summer 1793 (probably in June, and possibly in early July), just before he was put under arrest. He did not have enough time to finish or polish it. That is the reason why many passages remain elliptical or even equivocal, and why the structure of the essay is unbalanced. But these are not the only reasons why the 'Tableau général' is difficult to read: editorial blemishes were added to those contained in the manuscript, especially in the first edition.
Pierre Crépel and Jean-Nicolas Rieucau end their interesting article with the following conclusion [32]:-
The seeds of Condorcet's plan of applying calculus to political and moral sciences were already present in the early 1770s, when Condorcet located the "science of moral or political relations" within the branch of "physical mathematics." He developed it in various ways throughout the 1780s, most famously with his work on elections. In that respect, although the 'Tableau général' is indeed a blueprint for future work, it also constitutes a methodological synthesis of earlier researches. But its most specific features lie elsewhere. It is at the same time a mature text and, mostly because of the political circumstances in which it was written, quite a confused one, whose structure could have been improved. ... Retrospectively, one can imagine how much care Condorcet would have given to correcting and completing the 'Tableau général' had he had sufficient time for it. Under threat of impending banishment, at the climax of political instability, Condorcet chose to write quite an abstract text, almost the last which bore his signature. In no case can it be considered as a contingent work which he would have "taken lightly." Why did he decide to write it at that specific time? By presenting what he believed to be the true science of public happiness, his goal might have been "to rise above political debates," ... One can also suggest that Condorcet, who was already living half-clandestinely, meant to leave behind a legacy, with the intention of promoting a subject of enquiry which, as he wrote a few months later, "despite the successful attempts of some mathematicians, remains, as it were, in its early stages and ... [which] must open for the next generations a truly infinite source of enlightenment." One can guess that Condorcet considered himself as one of these "mathematicians."
Condorcet went into hiding and wrote a very interesting philosophical work Esquisse d'un tableau historique des progrès de l'esprit humain (1795). Oliver H Prior, who edited an edition of the Esquisse in 1938, writes in the Introduction (see [39]):-
Condorcet occupies a special place in the history of French thought. He is the last of the 'philosophes', and the only one who took an active part in the Revolution. He did not conceive a completely original system, but he did create a synthesis of all the theories of his predecessors. We can find in his writings the ideas of Voltaire, of Rousseau, of Turgot, of Helvetius, of Condillac, moulded bit by bit into a harmonious whole whose final expression is the 'Esquisse', a sort of philosophic résumé of the XVIII th century.
We present a version of Condorcet's Introduction to the Esquisse at THIS LINK.

In March 1794 he thought that the house in which he was hiding in Paris was being watched by his enemies and he no longer felt safe. He fled from Paris and after three days he was arrested and imprisoned on 27 March 1794. Two days later he was found dead in his prison cell and it is not known if he died from natural causes or whether he was murdered or took his own life.

John Herivel described Condorcet as follows [12]:-
... Condorcet was no politician. His uncompromising directness of manner and inability to suffer illogical windbags in silence made him many enemies and few friends. His weak voice, lack of oratorical powers, and tendency to bore the Convention by the excessive height of his arguments was one of the tragedies of the Revolution.
His life is summed up by Harry Burrows Acton (1908-1974) in [2] as follows:-
Wholly a man of the Enlightenment, an advocate of economic freedom, religious toleration, legal and educational reform, and the abolition of slavery, Condorcet sought to extend the empire of reason to social affairs. Rather than elucidate human behaviour, as had been done thus far, by recourse to either the moral or physical sciences, he sought to explain it by a merger of the two sciences that eventually became transmuted into the discipline of sociology.

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Written by J J O'Connor and E F Robertson
Last Update November 2020